WAEC Further Mathematics Past Questions & Answers - Page 45

221.

The area of a sector of a circle is 3\(cm^{2}\). If the sector subtends an angle of 1.5 radians at the centre, calculate the radius of the circle

A.

1 cm

B.

\(\sqrt{2}\) cm

C.

2 cm

D.

4 cm

Correct answer is C

The area of sector in radians = \(\frac{r^{2} \theta}{2}\)

\(3 cm^{2} = \frac{1.5 \times r^{2}}{2}\)

\(r^{2} = \frac{3 \times 2}{1.5} = 4\)

\(r = 2 cm\)

222.

Simplify \(8^{n} \times 2^{2n} \div 4^{3n}\)

A.

\(2^{-n}\)

B.

\(2^{1 - n}\)

C.

\(2^{n}\)

D.

\(2^{n + 1}\)

Correct answer is A

\(8^{n} \times 2^{2n} \div 4^{3n} = 2^{3n} \times 2^{2n} \div 2^{6n}\)

\(2^{2n + 3n - 6n}\)

= \(2^{-n}\)

223.

Which of the following is a singular matrix?

A.

\(\begin{pmatrix} 1 & 0 \\ 0 & 1 \end{pmatrix}\)

B.

\(\begin{pmatrix} 2 & 1 \\ 3 & 2 \end{pmatrix}\)

C.

\(\begin{pmatrix} 3 & 8 \\ 5 & 16 \end{pmatrix}\)

D.

\(\begin{pmatrix} 0 & 1 \\ 1 & 0 \end{pmatrix}\)

Correct answer is A

No explanation has been provided for this answer.

224.

Simplify \(\frac{^{n}P_{4}}{^{n}C_{4}}\)

A.

24

B.

18

C.

12

D.

6

Correct answer is A

\(^{n}P_{4} = \frac{n!}{(n - 4)!}\)

\(^{n}C_{4} = \frac{n!}{(n - 4)! 4!}\)

\(\frac{^{n}P_{4}}{^{n}C_{4}} = \frac{n!}{(n - 4)!} ÷ \frac{n!}{(n - 4)! 4!}\)

= \(4! = 24\)

225.

A committee of 4 is to be selected from a group of 5 men and 3 women. In how many ways can this be done if the chairman of the committee must be a man?

A.

15

B.

40

C.

70

D.

175

Correct answer is D

From the five(5) men viable for the position of the chairman, one of them must be selected.

This implies; 4 men and 3 women are open for committee membership.  

7 C\(_3\) = \(\frac{7!}{3!(7 - 3)!}\) = 

\(\frac{7⋅6⋅5⋅4⋅3⋅2⋅1}{3.2.1 \times 4.3.2.1}\)

= 35 \(\times\) 5 = 175